Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

The meniscus formed by mercury in a test tube is

A
convex

B
concave

C
no meniscus is formed

D
none of these

Solution

Convex meniscus is formed.
The reason for this happening is because of cohesion and adhesion. Meniscus is the curve of the upper surface in any liquid. Curving can be convex or concave. Cohesion is the ability of water molecules to cling to each other because of hydrogen bonds. Adhesion is the ability of water to cling to other polar surfaces, as a result of water's polarity.
So when water is placed into a glass container, surface tension attracts the water molecules to the sides of the glass and because adhesion overcomes the forces of cohesion the water climbs the glass slightly. This does not happen with Mercury because the opposite of water happens. The forces of cohesion are stronger than its attraction to the glass, it's adhesion. It have the opposite effect meaning it will be convex.
Question 2
1 / -0

Which molecule of a liquid has higher potential energy?

A
One at the centre of gravity of the liquid

B
One at maximum distance from centre of gravity of liquid

C
One in the surface film

D
One at the bottom of the vessel

Solution

Molecules at the surface feel an inward force due to strong cohesive forces then those inside the liquid because the inside molecules are surrounded by similar molecules, cohesive force acts in all directions making the net force on a single molecule equal to zero. But this is not the case with surface molecules, these molecules feels inward force, hence less stable i.e. have higher potential energy.
Question 3
1 / -0

In a container having water filled upto a height h, a hole is made in the bottom. The velocity of the water flowing out of the hole is:

A
independent of h

B
proportional to $$h^{1/2}$$

C
proportional to h

D
proportional to $$h^2$$

Solution

According to Torricelli's Theorem velocity of efflux i.e. the velocity with which the liquid flows out of a hole is equal to $$\sqrt{2gh}$$ where $$h$$ is the depth of the hole below the liquid surface.
So $$v\propto \sqrt{h}$$.
Question 4
1 / -0

A cylinder of height $$20$$m is completely filled with water. The velocity of efflux of water (in ms$$^{-1}$$) through a small hole on the side wall or the cylinder near its bottom is:

A
$$10$$ m/s

B
$$20$$ m/s

C
$$25.5$$ m/s

D
$$5$$ m/s

Solution

P.E. = K.E.
mgh = $$\dfrac {1}{2} mv^2$$
v = $$ \sqrt{2gh}= \sqrt{2 x 10 x 20}(Here g = 10 m/s^2)$$
$$= 20 m/s$$
Question 5
1 / -0

For flow of a fluid to be turbulent:

A
fluid should have high density

B
velocity should be large

C
reynold number should be less than 2000

D
both (a) and (b)

Solution

1) For turbulent flow both velocity and density of fluid should be high.
2) Value of reynold's number $${Re}>{4000}$$
note $${Re}<{2000}$$ is for laminar flow and $${2000}<{Re}<{4000}$$ transition flow.
Question 6
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The area of pistons in a hydraulic machine are $$5 c{m}^{2}$$ and $$625 c{m}^{2}$$. The force on the smaller piston so that a load of $$1250 N$$ on the larger piston can be supported, is X N. Find $$\dfrac{X}{2}$$ N.

A
5

B
10

C
1250

D
None of the above

Solution

We know that, $$Pressure = \dfrac{Force}{Area} $$

For Larger Piston, $$P_{l} = \dfrac{1250}{625} = 2N cm^{-2} $$
So, Pressure on the smaller piston should be equal to $$2Ncm^{-2}$$

So, Force on smaller piston $$X= Pressure \times Area= 2 \times 5 = 10N$$
$$\therefore \dfrac{X}{2}=\dfrac{10}{2}=5 N$$
Question 7
1 / -0

Two vessels $$A$$ and $$B$$ of cross-sections as shown in figure contain a liquid up to the same height. As the temperature rises, the liquid pressure at the bottom (neglecting expansion of the vessels) will:

A
increase in $$A$$, decrease in $$B$$

B
increase in $$B$$, decrease in $$A$$

C
increase in both $$A$$ and $$B$$

D
decrease in both $$A$$ and $$B$$

Solution

Volume will expand in both vessels due to increase in temperature, but the increased height will be less in vessel B, due to higher cross sectional area. However, the pressure will increase in both the vessels, hence correct answer is C
Question 8
1 / -0

A tank has a small hole at its bottom of area of cross-section a. Liquid is being poured in the tank at the rate $$Vm^3/s$$, the maximum level of liquid in the container will be(Area of tank A):

A
$$ \dfrac {V}{gaA}$$

B
$$ \dfrac {V^2}{2ga^2}$$

C
$$ \dfrac {V^2}{gAa}$$

D
$$ \dfrac {V^2}{2gaA}$$

Solution

At maximum level the discharge due to small hole will be equal pouring rate
$$V=va$$ , let the maximum height be H , assuming a<<A
$$V=a\sqrt{2gH}$$
$$H=\dfrac{V^2}{2ga^2}$$
Question 9
1 / -0

Two drops of the same radius are falling through air with a steady velocity of $$5\ \text{cm per sec}.$$ If the two drops coalesce, the terminal velocity would be

A
$$10\ \text{cm per sec}$$

B
$$2.5\ \text{cm per sec}$$

C
$$5\times (4)^{1/3}\ \text{cm per sec}$$

D
$$5\sqrt{3}\ \text{cm per sec}$$

Solution

If $$R$$ is radius of bigger drop formed, then

$$\dfrac {4}{3}\pi R^3 = 2\times \dfrac {4}{3}\pi r^3 $$ or $$R = 2^{1/3}r $$
As $$v_0 \propto r^2$$

$$\therefore \dfrac{v_{01}}{v_0} = \dfrac{R^2}{r^2}= \dfrac{(2^{1/3})^2}{r^2}= 2^{2/3}$$

or $$v_{01} = v_0 2^{2/3} = 5 (4)^{1/3}$$
Question 10
1 / -0

Figure shows a capillary rise $$h$$. If air is blown through the horizontal tube in the direction as shown then rise in capillary tube will be

A
$$= h$$

B
$$> h$$

C
$$< h$$

D
$$zero$$

Solution

If air is blown then by using Bernoulli equation we can conclude as the air is blown the pressure over capillary will reduce
and $$P_0=P+\rho gH$$ , where P is the pressure in horizontal tube, now as air is blown , P will decrease H will increase because $$P_o$$ is constant (atmospheric pressure)

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Mechanical Properties of Fluids Test - 28

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Question 1

convex

concave

no meniscus is formed

none of these

Solution

Question 2

One at the centre of gravity of the liquid

One at maximum distance from centre of gravity of liquid

One in the surface film

One at the bottom of the vessel

Solution

Question 3

independent of h

proportional to $$h^{1/2}$$

proportional to h

proportional to $$h^2$$

Solution

Question 4

$$10$$ m/s

$$20$$ m/s

$$25.5$$ m/s

$$5$$ m/s

Solution

Question 5

fluid should have high density

velocity should be large

reynold number should be less than 2000

both (a) and (b)

Solution

Question 6

5

10

1250

None of the above

Solution

Question 7

increase in $$A$$, decrease in $$B$$

increase in $$B$$, decrease in $$A$$

increase in both $$A$$ and $$B$$

decrease in both $$A$$ and $$B$$

Solution

Question 8

$$ \dfrac {V}{gaA}$$

$$ \dfrac {V^2}{2ga^2}$$

$$ \dfrac {V^2}{gAa}$$

$$ \dfrac {V^2}{2gaA}$$

Solution

Question 9

$$10\ \text{cm per sec}$$

$$2.5\ \text{cm per sec}$$

$$5\times (4)^{1/3}\ \text{cm per sec}$$

$$5\sqrt{3}\ \text{cm per sec}$$

Solution

Question 10

$$= h$$

$$> h$$

$$< h$$

$$zero$$

Solution

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